194 



E, I. Terekhin 



or, representing the second term of the equation as the difference between 

 the two sums, 



oo oo 



n = m + l n = no+l 



-2 2 (^n-p„+^n+Po-2U- 2 (^n-p„+^.+po-2g. 



n = /7o + l 



n = m + l 



Treating the obtained series exactly the same as for case (a), we ob- 

 tain 



oo p„ 



2j I ^/2-po+ ^/i+Po~2i„ I = 2 2j (Zn„-po+i~^n„+i)~ 



n = m + l 



P. 



~" 2j \''m-pa+i'~^m+i)' 

 1 = 1 



The error in this case is determined by the inequahty 



^^2 < 2" I ^max I 



Po Po "1 



2 2j (^no-po+J~"^no+i)"~ Zj (^m-p„+i~^m+i) 

 i=l 1=1 J 



(38) 



The relative value of the error can then be found 



a=^< 



All geoelectrical sections, for which the curves of apparent resistance 

 were calculated by the shortened method, for a sea-bottom apparatus, had 

 j5q = 1 (the layer lying directly under the water, greater than or equal to the 

 thickness of the Avater layer) the expressions for the errors were therefore 

 considerably simplified : 



^S^ ^—\ 5'rnax | (^m ^m + l)? 



^•^2 <-2 1 9max I [2 (/n„-/n„+i) -(^m -4l+l)]• 

 Replacing (/„-Z^+i) by Al^, and (/„„-Z„„+i) by Al^^^ we find the 

 expression for the relative error: 



